Here’s one way to think of anthropic reasoning. You’ll need an urn, and a stochastic process that can put balls in the urn.
For example, to think about safety vs. danger in the past, we make a stochastic process that is a toy model of a possibly-dangerous situation, but instead of people living we put a ball in the urn. So perhaps we flip a coin that has Safety written on one side and Danger on the other. If Safety, we put a ball in the urn. If Danger, we flip another coin between Nuclear War and No Nuclear War, and if No Nuclear War, we put a ball in the urn.
So from our perspective as the experimenter, when we try to draw a ball from the urn, there’s a 50% chance of Danger having come up, and a 25% chance that when we try to draw a ball from the urn, there will be nothing there, on account of Nuclear War. If we want to do simple anthropic reasoning from the perspective of the ball (sphairic reasoning?), then what we do is we condition on the ball being drawn from the urn. Conditional on this event, we know that Nuclear War did not happen, and we believe that Safety was twice as likely as Danger.
I only bring up this re-statement of your reasoning because I personally find this “stochastic process, condition on drawing a ball to get its perspective” framing useful for thinking about confusing anthropic stuff.
Here’s one way to think of anthropic reasoning. You’ll need an urn, and a stochastic process that can put balls in the urn.
For example, to think about safety vs. danger in the past, we make a stochastic process that is a toy model of a possibly-dangerous situation, but instead of people living we put a ball in the urn. So perhaps we flip a coin that has Safety written on one side and Danger on the other. If Safety, we put a ball in the urn. If Danger, we flip another coin between Nuclear War and No Nuclear War, and if No Nuclear War, we put a ball in the urn.
So from our perspective as the experimenter, when we try to draw a ball from the urn, there’s a 50% chance of Danger having come up, and a 25% chance that when we try to draw a ball from the urn, there will be nothing there, on account of Nuclear War. If we want to do simple anthropic reasoning from the perspective of the ball (sphairic reasoning?), then what we do is we condition on the ball being drawn from the urn. Conditional on this event, we know that Nuclear War did not happen, and we believe that Safety was twice as likely as Danger.
I only bring up this re-statement of your reasoning because I personally find this “stochastic process, condition on drawing a ball to get its perspective” framing useful for thinking about confusing anthropic stuff.